diff options
Diffstat (limited to 'sections')
| -rw-r--r-- | sections/conj_classes.tex | 9 | ||||
| -rw-r--r-- | sections/examples.tex | 2 |
2 files changed, 8 insertions, 3 deletions
diff --git a/sections/conj_classes.tex b/sections/conj_classes.tex index 4732e3c..446b70e 100644 --- a/sections/conj_classes.tex +++ b/sections/conj_classes.tex @@ -184,7 +184,6 @@ $(B_{i,j}, \beta_{i,j})$ to $(\Gamma'_n, g'_n)$. But this can be easily done by the fact, that $\cD$ has the amalgamation property. - It is important to note that $g'_n$ should be a finite function and once again, as it is an automorphism of a finitely generated structure, we may think it is simply a map from one generators of $\Gamma'_n$ to the @@ -240,9 +239,15 @@ and the above Theorem \ref{theorem:generic_aut_general}. \end{proof} + \begin{corollary} + Let $\cC$ be a Fraïssé class of finitely generated $L$-structures with WHP + and canonical amalgamation. Then $\Flim(\cC)$ has a generic automorphism. + \end{corollary} + \subsection{Properties of the generic automorphism} - This key theorem yields some corollaries and we present one of them below. + The key Theorem \ref{theorem:key-theorem} yields some corollaries and we + present one of them below. Let $\cC$ be a Fraïssé class of finitely generated $L$-structures with weak Hrushovski property and canonical amalgamation. diff --git a/sections/examples.tex b/sections/examples.tex index d9101de..438f3cb 100644 --- a/sections/examples.tex +++ b/sections/examples.tex @@ -120,7 +120,7 @@ \end{figure} \vspace{0.5cm} - On the other hand $\cL$ cannot have $WHP$. This follows from the fact that + On the other hand $\cL$ cannot have WHP. This follows from the fact that that only automorphism of a finite linear ordering is identity, so we cannot extend a partial automorphism sending exactly one element to some distinct element. However, in this case, generic automorphism exists |